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Now a Major Motion Picture .... well, how about a YouTube sequence of 20 VIDEOS, look for Mathematical Modeling and Computational Calculus I.

This book will take you from not being able to spell calculus to doing calculus just the way I did it for twenty years as an engineer at high tech firms like Lockheed and Stanford Telecom. You will learn how physical processes are modeled using mathematics and analyzed using computational calculus. Systems studied include satellite orbits, the orbits of the earth and moon, rocket trajectories, the Apollo mission trajectory, the Juno space probe, electrical circuits, oscillators, filters, tennis serves, springs, friction, automobile suspension systems, lift and drag, and airplane dynamics. And not a single theorem in sight.

This book focuses on differential equation models because they are what scientists and engineers use to model processes involving change. Historically, this has presented a big problem for science education because while the models are easy enough to create, solving the differential equations analytically usually requires advanced mathematical techniques and their clever application. But, that was before computers; now, with computers, solutions to differential equations can be computed directly, without the need of theorems or any advanced mathematics, using the formula distance equals velocity times time. It's just that simple. The book will show you how it's done.

Is there a trick here? Of course, here it is: suppose you, as Newton did, want to compute the trajectory of a falling apple, and let's say that the apple's acceleration is constant and equals 10 meters/second/second. So the apple's velocity at the instant it falls is 0 m/s, after 1 second it is 10 m/s, after 2 seconds it is 20 m/s, and after t seconds it is v(t) = 10*t m/s.

You want to know the distance d(t) the apple has fallen after t seconds. This is the problem calculus was developed to solve, that is, given a velocity function v(t), determine the corresponding distance function d(t). To solve it Newton proved theorem after theorem and finally came up with a formula that gives the answer, in this case d(t) = 5*t*t.

But computational calculus bypasses all the theorems and formulas: to calculate how far the apple has fallen after 8 seconds, i.e. d(8), it just subdivides the interval of interest, 8 seconds in this case, into small sub-intervals, say 1 second each, and since the apple's velocity is known at the start of each sub-interval, it uses that velocity to estimate how far the apple falls in the sub-interval using the formula, get ready for it, distance equals velocity times time. The distances for all the sub-intervals are added and that's how far the apple falls in 8 seconds. Capiche?

This is the way it is actually done in the engineering world.

There are two big advantages to the computational method, first, it is very easy to learn, there is only one formula, distance = velocity times time. Second, for most velocity functions v(t) you can't use Newton's method because there is no formula for d(t) that works, none exist. But you can always use computational calculus, no matter how complex the problem, you just compute away and get the answer. Computational calculus has transformed engineering and science.

Well, just how many calculations do you have to do? Ans: lots. So in the book we do the first few calculations by hand, and then show you how to automate the process using FREEMAT, a free clone of MATLAB. Using FREEMAT you can write the instructions for a calculation once and then perform the calculation 10,000 times using the statement FOR i=1:10000, the calculation, END, and t

• Sales Rank: #1687452 in Books
• Published on: 2013-08-01
• Binding: Spiral-bound
• 182 pages

Review
Students who will continue to study higher math will still need to take calculus or higher courses that teach the theoretical math, but this course might be the bridge that helps students become enthused enough about calculus to continue on to higher levels of math. It also might be a good course for those who want to understand what calculus is all about and how it is used even if they don t intend to take any higher math courses. --cathyduffyreviews.com

About the Author
The author has a PhD from Berkeley and spent twenty years as a research engineer in high tech firms like Honeywell Aerospace Division, Lockheed, and Stanford Telecom.

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1 of 1 people found the following review helpful.
This guy know how to teach calculus
By shootn'scoot
I really appreciate CWT. Professor Flannery understands how a guy like me learns. Simple small lessons with lots of practice. I'll leave the intuitive leaps to the Euler's of the world. I'll just baby step through it. Thank you Mr. Flannery. I really have benefited from your approach.

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How many angels can dance on the head of a pin? People have toyed with that question for centuries. Now Barbara Helen Berger's newest book prompts fascinating new questions: What if there was a whole city on the head of a pin? And the angels there thought they lived in the best, and only city in the universe? Until someone discovered there were other pins. And other cities. With angels dancing in every one!

Author/artist Barbara Helen Berger provides a magical, musical glimpse of worlds within worlds, where angels dance and the possibilities are endless.

• Sales Rank: #1501879 in Books
• Published on: 2000-03-06
• Released on: 2000-03-06
• Original language: English
• Number of items: 1
• Dimensions: 11.00" h x .32" w x 8.96" l,
• Binding: Hardcover
• 32 pages

From Publishers Weekly
Berger (Grandfather Twilight) offers a pretty but vacuous riff on the originally satirical question "How many angels can dance on the head of a pin?" by positing dreamy worlds within worlds of tiny, pin-dwelling angels. Her story opens with the question, "What if there was a city on a pin?"; the accompanying art shows a small-town street, with people and pets--all of them with wings, apparently angels. In the foreground, an elderly woman angel sees a pincushion in a dressmaker's window. The next pages home in on the pincushion, where the head of each pin is the site of a whole city of tiny angels. The plot is thin to the point of brittle: the angels on the pin-city think theirs is the only one in the world, then a child using a telescope spies another city on a pin, contact is made and a celebration begins. Berger's mixed-media paintings create a light and lively atmosphere where angels of all ages and nationalities boogie-woogie ("Shimmy shimmy hip hop, and cha-cha-cha") in mid-air, rejoicing, "Hey wow, look! We're not alone!" The framing story reprises this theme, returning to illustrations of the elderly woman, now joined by a dapper old gent in a top hat--and, suggesting the circularity of the premise, a child can be seen gazing through a telescope. Given that Berger makes no particular use of the angel motif (these could just as well be miniature people), the net effect is that of an extended daydream. Ages 4-8. (Feb.)
Copyright 2000 Reed Business Information, Inc.

From School Library Journal
PreSchool-Grade 1-A story that ponders the nature of existence in an entire city atop the head of a pin. The winged inhabitants of the pin-top metropolis wonder if there are worlds beyond their own, until a resident spies another community on a neighboring pin. The din from the celebration of their mutual discovery is heard throughout the universe and even more civilizations respond from all over the pincushion and beyond. This revelation helps people to realize that, "Hey wow, look! We're not alone!" Fanciful acrylic, colored-pencil, and pastel illustrations depict a benign multiethnic cast living in pastel-shaded worlds offset by backdrops of deep blues and blacks. While the whimsical yet mysterious pictures will appeal to youngsters, the spare text may leave listeners wishing for more. Fairly deep philosophical concepts are touched upon in this light picture-book romp, creating a certain dissonance between topic and treatment. Children, however, may be oblivious to such considerations and enjoy the book as a light confection as suggested by the visual presentation.
Rosalyn Pierini, San Luis Obispo City-County Library, CA
Copyright 2000 Reed Business Information, Inc.

From Kirkus Reviews
``What if there was a city on a pin?'' Berger (A Lot of Otters, 1997, etc.) asks curiously (if ungrammatically) in this fanciful musing. The city is no bigger than a speck of dust on the head of a pin, but for its inhabitants, it is all there is, and sometimes it makes them lonesome. Then they find another city, travel there, and the boogie-woogie begins: bebop, shimmy, cha cha cha. The cityscapes look like as if they are made of pastel spun sugar, and the figures are recognizably skateboarders, bikers, church ladies, childrenbut they all have wings. The mayor, refulgent in his formal dress, has red wings, a black-and-white dog has pink ones, and the two-stepping cowpokes sport green and gold ones. All this dancing takes place in the streets, above the buildings, and in the lapis-colored, starry sky between the cities. The book's messagethat we are not aloneisn't hammered but sort of tapped gently. The question, ``How many angels can dance on the head of a pin?'' is as least as old as Aquinas and forms the colophon here, leading readers into a dream-scented landscape. (Picture book. 4-8) -- Copyright ©1999, Kirkus Associates, LP. All rights reserved.

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5 of 5 people found the following review helpful.
Beautiful illustrations - but. . .
By A Customer
I am a big Barbara Helen Berger fan, and as such I was surprised to find myself dissapointed by this book. The illustrations are just as beautiful as her other works, but there was no real story, just a short "we are not alone" message. I was quickly bored, and so was my daughter. However, I did notice my daughter making up her own story as she leafed through the pages. All in all, though, I much prefer this author's other books.

4 of 4 people found the following review helpful.
Dreamy and delightful
By A Customer
Barbara Berger creates some of the most beautiful imagery in children's picture books, and her spare, evocative prose is the perfect complement to the misty, fanciful illustrations. What a fabulous way to inspire children to think in new and creative ways, while experiencing the joy and exuberance of the imagination. This book is perfect for any child.

1 of 1 people found the following review helpful.
beautiful
By Amazon Customer
My daughter and I loved Grandfather Twilight (she more than me), and so I looked and found this one. It's not religious, except for 'angels,' but about reaching out and connecting to others. The pictures are beautiful, and the first time I read it, I nearly cried. It reminded me of the kind of pure simple hope I had a child, that someday we might meet people from another world, and we would reach out to each other with no fear, only sheer joy at knowing we aren't alone. What a wonderful story to wind down an evening.

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• Published on: 2012
• Binding: Paperback

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• Sales Rank: #3930102 in Books
• Published on: 2014-06-21
• Original language: English
• Number of items: 1
• Dimensions: 9.00" h x .58" w x 6.00" l, .75 pounds
• Binding: Paperback
• 230 pages

About the Author
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Seek first the kingdom of God and His righteousness.

There are few dreams more spiritually intoxicating than the dream of being used by God to start a new community of Christ that skillfully brings the restorative gospel to a lost and broken city. Something which feels like a spiritual landslide that starts with lostness and ends in an avalanche of new congregations multiplying and transforming community after community into which they unmistakably seep.

Authors Jeff Christopherson and Mac Lake call readers to imagine a movement that vividly remembers the insubstantial days of a mustard seed with a sense of awe and wonder when looking at the indescribable harvest that stands all around. Though the kingdom of God can't be forced by superficial methods, the good news is that when you move past the threshold of your competency and comfort, you find yourself in the very spot where God can use you like no other.

What wouldn’t you sacrifice to be a part of something that only could be described as a God-honoring gospel movement?

• Sales Rank: #637884 in eBooks
• Published on: 2015-05-12
• Released on: 2015-05-12
• Format: Kindle eBook

About the Author
Jeff Christopherson is about fostering Kingdom movements of reproducing churches that transform neighborhoods and the world with the gospel of Jesus Christ. Jeff is the North American Mission Board's VP for the Send City Network and Regional VP for Canada. Also the author of Kingdom Matrix: Designing a Church for the Kingdom of God, he and his wife, Laura, live in Oakville, Ontario. They have two children.

Mac Lake is the Chief Launch Officer of The Launch Network, a Church Planting Network based out of Atlanta, Georgia. Also the author of Growing Small Group Leaders, he and his wife Cindy have three children Brandon, Jordan and Brianna.
 

Most helpful customer reviews

4 of 4 people found the following review helpful.
Move Over February!
By RB Ferguson
In this book Jeff Christopherson and Mac Lake have not revealed the “keys” to the kingdom, rather they have illuminated some of the “secrets” of the kingdom lived out by Jesus himself. We only have two occasions in the New Testament when Jesus used the word “church”. But each gospel reverberates, dozens of times, with his use of the term “kingdom”. Rest assured these secrets are not “pie-in-the-sky” platitudes but gospel truth able to assist church planters in planting churches with a "huge degree of practicality". My favorite book on disciple making (and church planting) has always been Robert Coleman’s Master Plan of Evangelism. I read it every year in the month of my birth. Move over February, I think I found another classic in the making that I need to revisit again and again and again…..

2 of 2 people found the following review helpful.
Have your highlighter handy with this one!
By Joseph H Outlaw
Answering the call to plant a church or to be a church planting team member is not an easy journey, but Jeff and Mac have provided a resource in Kingdom First that is an easy read and an extremely practical tool. What appears in the pages of Kingdom First I have been blessed to live out- both in serving on a core group with Mac at a church plant in Myrtle Beach, SC, and as a planting support player with Jeff through the North American Mission Board. Both men share their passion for planting as a key to sustainable Kingdom growth thoughtfully and pragmatically. Their heart leaps out as I read it! Kingdom First reads as a gentile playbook for planting churches that plant churches. I think those called to plant churches or to serve as a church planting team member will have a hard time putting this book down or leaving its pages black and white. It's that good!

1 of 1 people found the following review helpful.
A beautiful blend of depth and relevance!
By Tim Wheat
It is rare to be able to have a resource on church planting that lays both a solid theological foundation combined with relevant practical expression in one work. Christopherson and Lake have given us both in Kingdom First. From a missiological perspective, this book will expand your ability to see the necessary components to advance the Kingdom through a God-glorifying movement of establishing new communities of faith. From a practitioner's perspective, you will see a clear path to take in understanding and preparing for the high call of church planting. This book is both a beautiful blend of depth and relevance. These two guys have produced a work that not only serves as a guide for church planting but will challenge and inspire any leader and disciple-maker. Every pastor and potential church planter should make this a "must read" and "multiple-read" book!

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• Sales Rank: #10690521 in Books
• Published on: 2001-03-01
• Original language: German
• Number of items: 1
• Dimensions: 8.43" h x 1.06" w x 5.28" l,
• Binding: Hardcover

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How, if at all, do Muslims and non-Muslims differ? The question spurs spirited discussion among people the world over, in Muslim and non-Muslim lands alike, but we still lack answers based on sound empirical evidence. This book engages a set of the biggest issues using rigorous methods and data drawn from around the globe. It reveals that in some areas Muslims and non-Muslims differ less than is commonly imagined, and shows that Muslims are not unusually religious or inclined to favor the fusion of religious and political authority. Nor are Muslims especially prone to mass political violence. Yet in some areas Muslims and non-Muslims diverge: Gender inequality is more severe among Muslims, Muslims are unusually intolerant of homosexuality and other controversial behaviors, and democracy is rare in the Muslim world. Other areas of divergence bear the marks of a Muslim advantage: Violent crime and class-based inequities are less severe among Muslims than non-Muslims. Committed to discovering social facts rather than either stoking prejudices or stroking political sensibilities, Are Muslims Distinctive? represents the first major scientific effort to assess how Muslims and non-Muslims differ--and do not differ--in the contemporary world. Its findings have vital implications for human welfare, interfaith understanding, and the foreign policies of the United States and other Western countries.

• Published on: 2011
• Number of items: 2
• Binding: Paperback

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